Symmetric pairs with finite-multiplicity property for branching laws of admissible representations

Abstract

We accomplish the classification of the reductive symmetric pairs $(G,H)$ for which the dimension of the space $\mathrm{Hom}_{H}(\pi|_{H}, \tau)$ of $H$-intertwining operators is finite for any irreducible smooth representation $\pi$ of $G$ and for any irreducible smooth representation $\tau$ of $H$.